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The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.
The Measurement of Health and Health Status: Concepts, Methods and Applications from a Multidisciplinary Perspective presents a unifying perspective on how to select the best measurement framework for any situation. Serving as a one-stop shop that unifies material currently available in various locations, this book illuminates the intuition behind each method, explaining how each method has special purposes, what developments are occurring, and how new combinations among methods might be relevant to specific situations. It especially emphasizes the measurement of health and health states (quality-of-life), giving significant attention to newly developed methods. The book introduces technically complex, new methods for both introductory and technically-proficient readers. - Assumes that the best measure depends entirely on the situation - Covers preference-based methods, classical test theory, and item response theory - Features illustrations and animations drawn from diverse fields and disciplines
This 1997 book discusses the shift to quantitative perception which made modern science, technology, business practice and bureaucracy possible.
This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life—for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers. Mathematical symmetry is well known, as can be inferred from Hirschfeld’s simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato’s dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.
This book focuses on quantitative reasoning as an orienting framework to analyse learning, teaching and curriculum in mathematics and science education. Quantitative reasoning plays a vital role in learning concepts foundational to arithmetic, algebra, calculus, geometry, trigonometry and other ideas in STEM. The book draws upon the importance of quantitative reasoning and its crucial role in education. It particularly delves into quantitative reasoning related to the learning and teaching diverse mathematics and science concepts, conceptual analysis of mathematical and scientific ideas and analysis of school mathematics (K-16) curricula in different contexts. We believe that it can be considered as a reference book to be used by researchers, teacher educators, curriculum developers and pre- and in-service teachers.
The Mathematics of Measurement is a historical survey of the introduction of mathematics to physics and of the branches of mathematics that were developed specifically for handling measurements, including dimensional analysis, error analysis, and the calculus of quantities.
The Sage Handbook of Measurement is a unique methodological resource in which Walford, Viswanathan and Tucker draw together contributions from leading scholars in the social sciences, each of whom has played an important role in advancing the study of measurement over the past 25 years. Each of the contributors offers insights into particular measurement related challenges they have confronted and how they have addressed these. Each chapter focuses on a different aspect of measurement, so that the handbook as a whole covers the full spectrum of core issues related to design, method and analysis within measurement studies. The book emphasises issues such as indicator generation and modification, the nature and conceptual meaning of measurement error, and the day-to-day processes involved in developing and using measures. The Handbook covers the full range of disciplines where measurement studies are common: policy studies; education studies; health studies; and business studies.
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.